When we travelled to Sitka in June of 2003, the weather was cold and rainy, the transfer from ship to port took forever, and we only had six hours in port. It was absolutely the BEST port that we saw in Alaska. That is saying a lot since every port was very special and unique for us.
In Sitka we took a wildlife tour with one of the island residents. Our guide was named Bruce... I forget his last name but he was a great guide and I think that I still have his contact information at home. You can pick up these tours for $15-20 right at the port for a 2-3 narrated bus tour of the island. Depending on season, you can see all sorts of marine and land wildlife. There are more bears in Sitka than there are people though we didn't see any while we were there. We did see more bald eagles than you could even believe. They were everywhere. It was beyond breathtaking. My brother has a 4 second clip of video from his camera where you can clearly count a dozen bald eagles fly by less than 200 feet away. Bruce shared some of his locally caught and smoked salmon with us as we toured around some of the easily accessible locations in Sitka. If you have more time there, you can do much more. Fishing (sea, river, or lake) if that is your thing, hiking, biking, kayaking is all close by.
After our brief wildlife tour, Bruce dropped us off at a place that rents tandem sea kayaks. We set out across the harbor to tool around the islands. The harbor is all sheltered from the open sea so the water was never too rough. You have a skirt on your kayak to protect you from the frigid water. There is a very picturesque lighthouse and many beautiful homes located on tiny islands dotted around the bay. It was a tiny bit intimidating kayaking in deep water than more than likely had whales swimming around in it. The tandem kayak might work for you, if you don't mind paddling your friend with the bad back around for a while. He/she could hold the camera and get lots of great shots.
Bring your digital camera or camcorder to Sitka even if you don't take it anywhere else. There are some really incredible shots that we still look back on from that trip. Most of them are from Sitka. Have a great time!